MATHEMATICS · Multi-part · AP · AP Statistics · Exploring One-Variable Data · Exploring One-Variable Data
Problem
Two factories, P and Q, manufacture identical bolts. Forty bolts from each factory were weighed, and it was found that both samples had the same mean weight of 50 g. For the two factories the following measures of spread were obtained:
Factory P: variance =64 g2 (standard deviation =8 g)
Factory Q: variance =100 g2 (standard deviation =10 g)
Answer the following questions.
(i) If the weight limits for the bolts are 50 g ± 6 g, determine, with reason, which factory is more likely to produce bolts within the specified limits.
(ii) Explain briefly why the standard deviation is preferred over the variance when comparing the consistency of the two factories.